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Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =

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Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   16 Aug 2018, 05:16
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Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

Source: www.GMATinsight.com
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B
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PKN
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   16 Aug 2018, 05:42
GMATinsight wrote:
Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

Source: https://www.GMATinsight.com


Question stem:- Max(a*b)=?

St1:- a and b are prime numbers.

There are infinite numbers of prime numbers in number system.
So, the value of the product of two prime numbers is not unique.
Insufficient.

St2:- a+b = 10
Since prime numbers, by definition are positive in nature.
And the product a*b is maximum when a and b are maximum satisfying the given condition.
So, a=b=5 yields the max(a*b).
we got an unique value of a*b, hence sufficient.

Ans. (B)
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sachinkumardalal1303
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   16 Aug 2018, 05:49
To find. Maximum value of a*b
1) in first v r given a and b r prime numbers
But there r infinite prime numbers so v can't find out maximum value of a*b
So 1) is insufficient
Means answers would be among b,c,and e

2) v r given a+b =10. From which v can use hint and trial method and get that 5*5 can give us maximum value of a*b

So 2) is sufficient and our answer is b

ANSWER b

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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   16 Aug 2018, 05:50
To find. Maximum value of a*b
1) in first v r given a and b r prime numbers
But there r infinite prime numbers so v can't find out maximum value of a*b
So 1) is insufficient
Means answers would be among b,c,and e

2) v r given a+b =10. From which v can use hint and trial method and get that 5*5 can give us maximum value of a*b

So 2) is sufficient and our answer is b

ANSWER b

Posted from my mobile device
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   16 Sep 2018, 08:36
a+b=10
a*b-> max

ab=a(10-a)
f'(x)=10-2a => a=5; b=10-a => b=5

a*b=25
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   03 Dec 2018, 04:55
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PKN wrote:
GMATinsight wrote:
Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

Source: https://www.GMATinsight.com


Question stem:- Max(a*b)=?

St1:- a and b are prime numbers.

There are infinite numbers of prime numbers in number system.
So, the value of the product of two prime numbers is not unique.
Insufficient.

St2:- a+b = 10
Since prime numbers, by definition are positive in nature.
And the product a*b is maximum when a and b are maximum satisfying the given condition.
So, a=b=5 yields the max(a*b).
we got an unique value of a*b, hence sufficient.

Ans. (B)



Hi there!

Sorry but in statement number 2 you say "Since prime numbers.." But unless you use statement A, you cannot tell if a and b are prime numbers. They could be any number: 7+3 / 8+2 / 9+1

Can you kindly explain to me how you came up with the fact that they are both prime numbers?

Also another question (more general): aren't a and b supposed to be DIFFERENT numbers since they are defined with different variables?

Thank you very very much :)
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   03 Dec 2018, 10:12
oblivion441 wrote:
PKN wrote:
GMATinsight wrote:
Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

Source: https://www.GMATinsight.com


Question stem:- Max(a*b)=?

St1:- a and b are prime numbers.

There are infinite numbers of prime numbers in number system.
So, the value of the product of two prime numbers is not unique.
Insufficient.

St2:- a+b = 10
Since prime numbers, by definition are positive in nature.
And the product a*b is maximum when a and b are maximum satisfying the given condition.
So, a=b=5 yields the max(a*b).
we got an unique value of a*b, hence sufficient.

Ans. (B)



Hi there!

Sorry but in statement number 2 you say "Since prime numbers.." But unless you use statement A, you cannot tell if a and b are prime numbers. They could be any number: 7+3 / 8+2 / 9+1

Can you kindly explain to me how you came up with the fact that they are both prime numbers?

Also another question (more general): aren't a and b supposed to be DIFFERENT numbers since they are defined with different variables?

Thank you very very much :)


Bunuel VeritasKarishma

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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   12 Aug 2020, 13:40
ParthSanghavi wrote:
oblivion441 wrote:
PKN wrote:
GMATinsight wrote:
Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

Source: https://www.GMATinsight.com


Question stem:- Max(a*b)=?

St1:- a and b are prime numbers.

There are infinite numbers of prime numbers in number system.
So, the value of the product of two prime numbers is not unique.
Insufficient.

St2:- a+b = 10
Since prime numbers, by definition are positive in nature.
And the product a*b is maximum when a and b are maximum satisfying the given condition.
So, a=b=5 yields the max(a*b).
we got an unique value of a*b, hence sufficient.

Ans. (B)



Hi there!

Sorry but in statement number 2 you say "Since prime numbers.." But unless you use statement A, you cannot tell if a and b are prime numbers. They could be any number: 7+3 / 8+2 / 9+1

Can you kindly explain to me how you came up with the fact that they are both prime numbers?

Also another question (more general): aren't a and b supposed to be DIFFERENT numbers since they are defined with different variables?

Thank you very very much :)


Bunuel VeritasKarishma

Please Help



Statement 1 is clearly insufficient

Statement 2 : Not necessarily we need to look for prime, Given a+b =10, a multiple of a number is greater of its sums digits when both digits are same. This is a theory, You can try with any number. thus sum of 10 will be greater with digits 5+5 =10, 5*5= 25
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   18 Aug 2020, 01:27
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Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

----------

Question for #2 (echoing one of the previous posts).

2) a + b = 10

a and b could be:
- 9 and 1
- 8 and 2
- 7 and 3
- 6 and 4
- 5 and 5

I understand that 5 and 5 would yield the max a*b but is ok to assume these two numbers ARE A&B in GMAT when there are 4 other pairs possible based on statement #2? Pls help :)

----

Bunuel VeritasKarishma
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   21 Aug 2020, 03:33
Expert Reply
camilla777 wrote:
Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

----------

Question for #2 (echoing one of the previous posts).

2) a + b = 10

a and b could be:
- 9 and 1
- 8 and 2
- 7 and 3
- 6 and 4
- 5 and 5

I understand that 5 and 5 would yield the max a*b but is ok to assume these two numbers ARE A&B in GMAT when there are 4 other pairs possible based on statement #2? Pls help :)

----

Bunuel VeritasKarishma


Since we are looking for the maximum value of a*b, we do need to pin point to the values of a and b which yield us the max value of a*b. Since 5 and 5 do that, it works. Though I am never happy with DS questions asking for max/min values. When do you have enough information? As you keep adding constraints, max/min values keep changing.
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = [#permalink] New post   12 Dec 2022, 05:10
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